Question

Which of the following statements must be true?

A. ∠ABC = 87°
B. BD bisects ∠ABC
C. AB = BC
D. The circumcenter lies on BD.

Answer 1

The statement 'BD bisects ∠ABC' must be true.

Step-by-step explanation:

To determine which of the given statements must be true, let's analyze each option:

A. ∠ABC = 87°:

This statement may or may not be true. We cannot conclude the exact measure of ∠ABC without further information.

B. BD bisects ∠ABC:

This statement must be true. If BD bisects ∠ABC, then it divides the angle into two congruent angles, making it true.

C. AB = BC:

This statement may or may not be true. We cannot conclude the equality of AB and BC without further information.

D. The circumcenter lies on BD:

This statement may or may not be true. The circumcenter of a triangle does not necessarily lie on any specific segment within the triangle.

Therefore, the only statement that must be true is B. BD bisects ∠ABC.